Location sorting and endogenous amenities: Evidence from Amsterdam

Motivation

Amenity, sorting, inquality

• Socioeconomic inequality is tightly linked to residential choice.

• Important mechanism that amplifies this inequality: Endogenous amenity.

Amenity is endogenous

• (Local) Amenity is not a fixed value but an equilibrium outcome.
  • Households make location choices based on their heterogeneous preferences on different dimension of amenities.
  • Local amenities cater to the need of the demographic composition in their neighborhoods.

Thus, fully characterizing this nature of endogenous amenity is important in understanding its effect on welfare inquality.

Challenges in prior literature

Crude understanding of the nature of amenity

• Amenities are typically modeled as a one-dimensional object (aggregating the variety of location characteristics).

Aggregation of amenity into single-index does not allow…

• Households’ diverse tastes for different consumption amenities (horizontal differentiation of neighborhood on the demand side).

• Fims providing such amenities cater to this heterogeneity (differential supply-side responses to consumer heterogeneity).

• A more full picture to help design policies that alleviate urban inequality.

Possibly due to lack of data, model, shock, etc.

Research question

How does preference heterogeneity over multiple endogenous consumption amenities shape with-city residential sorting and inequality?

• How does significant change in local residential composition (e.g. tourism in Amsterdam) affect local residential markets (rental price) and amenity markets (change in local amenities for residents and tourists).

Methodology

“Reduced-form” regression to show stylized facts and motivation

• Shift-share IV regression to causally estimate the impact of mass tourism on local housing and amenity markets.

• Identification: “Shift” (time variation in worldwide demand for STR) - “Share” (neighborhood-level exposure to tourism using spatial distribution of historic monuments)

  • Higher STR entry led to higher rental price.
  • Amenities have tilted toward tourists and away from locals.
  • The composition of residents has changed heterogeneously across neighborhoods.

“Structural model”

• Build a dynamic model of a city’s rental market that consists of:

  1. Heterogeneous households and tourist making location decisions,
  2. Landlords who can rent their units to local or tourists,
  3. A market for amenities that microfounds how the composition of amenities endogenously responds to the composition of locals and tourists.

Related literature

Spatial equilibrium model: Benchmark to study spatial inequality across and within cities

• Focus on within-city margin but silent on the mechanisms through which specific amenities are provided: Bayer et al. (2007); Guerrieri et al. (2013); Ahlfeldt et al. (2015); Su (2022).

• Impose structure on amenity but lack heterogeneity in residents’ preferences over amenities or collapse amenities into a single quality index: Couture et al. (2021); hoelzlein (2020); Miyauchi et al. (2021).

  • This paper contributes by allowing for preference heterogeneity over multiple and differentiated amenities.

STR industry: Simultaneously studying effects of tourism on both residential and amenity markets

• Calder-Wang (2021): Distributional effects of STR industry on NYC rental market.

• Allen et al. (2021): The effects of seasonal tourism on prices of goods and amenities borne by residents of Barcelona.

Discrete-choice tools: Euler Equation in Conditional Choice Probabilities estimator for dynamic estimation

• Hotz and Miller (1993); Arcidiacono and Miller (2011); Aguirregabiria and Magesan (2013); Scott (2013); Kalouptsidi et al. (2021b); Hsiao (2021); Traiberman (2019); Humlum (2021); Diamond, McQuade and Qian (2019); Davis et al. (2019); Davis et al. (2021).

Data overview

Individual-level data: Statistical bureau of the Netherlands’ Centraal Bureau voor de Statistiek (CBS)

• Construct a panel of residential history for the universe of individuals \(+\) household-level demographics from tax return data (income, education, employment status, etc).

Housing unit data: CBS tax appraisal panel and national rent survey

• Universe of residential housing units (property value, occupant’s tenancy status, rental prices, etc).

Neighborhood-level data: Amsterdam City Data (ACD)

• Two level of geographic units: 99 neighborhoods (wijk) in 25 larger districts (gebied).

• ACD: Annual neighborhood-level outcomes (ethnic, income, rich set of consumption amenities, city-level tourist inflows).

• Set of amenities are narrowed down to six: Restaurants, bars, food stores, non-food stores, nurseries, and “touristic amenities.”

Short-term rental (STR) listings: Airbnb listing-level observations (geo-coordinates, prices, etc)

Final sample: Annual panel of location choices and characteristics for 2008-2018 in 22 districts.

Descriptive evidence

• Fact 1: Tourists and STR listings have grown dramatically and sprawled across Amsterdam.

• Fact 2: Rents have increased more in neighborhoods with more STR entry.

• Fact 3: Amenities have tilted towards tourists and away from locals.

• Fact 4: The composition of residents has changed heterogeneously across neighborhoods.

Economic model 1: Endogenous amenities

Notation: \(J+1\) locations; \(K\) types of locals and tourist type \(T\); \(S\) sectors; Population composition \(M_{jt} \equiv [M_{jt}^1, ... , M_{jt}^K, M_{jt}^T]'\); Amenities \(a_{jt} \equiv [N_{1jt}, ..., N_{sjt}]'\)

Demand for amenities

Household with Cobb-Douglas (CD) perferences over housing \(H\) and amenities \(C\), CD preferences across amenity sector and CES preferences over varieties within a sector:

\[q_{isjt} = \sum_k q_{isjt}^k M_{jt}^k, \quad \text{where} \, \, q_{isjt}^k = \frac{\alpha_s^k \phi^k \omega_t^k}{p_{isjt}}\left( \frac{p_{isjt}}{P_{sjt}}\right)^{1-\sigma_s}\]

Supply of amenities (monopolistic competition, same marginal cost, free entry): Zero-profit condition

\[(p_{sjt} - c_{sjt}) q_{sjt} = \underbrace{F_{sjt}(N_{jt})}_{\text{Fixed cost per period}}, \quad \text{where} \, \, N_{jt} = \sum_s N_{sjt}.\]

Equilibrium amenities: Adding up equations above gives market clearing condition back

\[N_{sjt} = \frac{1}{\sigma_s F_{sjt}} \sum_k \alpha_s^k \phi^k \omega_t^k M_{jt}^k, \quad a_{jt}=A(M_{jt})\]

Economic model 2: Housing supply

• Total housing stock (measured in units of floor space) \(H_{jt}\) is assumed to be inelastic in the short-rn and follows an exogenously determined path over time. Justfication

• A continuum of absentee landlords make a binary choice between renting in the long-term market (LT) or in the short-term market (ST).

An individual landlord’s problem

\[\max\{ \alpha \cdot \overbrace{\gamma_{jt}}^{\text{LT income}} + \varepsilon_{LT}, \, \, \alpha \cdot \underbrace{p_{jt}}_{\text{ST income}} - \overbrace{\kappa_{jt}}^{\text{operating cost}} + \varepsilon_{ST} \},\]

Housing supply in each location (\(\varepsilon \sim \text{T1EV}\))

\[H_{jt}^{LT,S} (\gamma_{jt}, p_{jt}) = \frac{\exp(\alpha \gamma_{jt})}{\exp (\alpha \gamma_{jt}) + \exp(\alpha p_{jt} - \kappa_{jt})} H_{jt},\]

\[H_{jt}^{ST,S} (\gamma_{jt}, p_{jt}) = H_{jt} - H_{jt}^{LT,S} (\gamma_{jt}, p_{jt}).\]

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Economic model 3-1: Housing demand (locals)

Dynamic location choice of locals

• Invidual state variables: Location \(j_{it-1}\) and Tenure \(\tau_{jt-1}\).

• Aggregate state variables: Rent \(\gamma_t\), Amenities \(a_t\), Exogenous location attributes \(b_t\), and unobservable factors \(\zeta_t\).

Household \(i\)’s dynamic problem (value function)

\[V^k (x_{it}, \varepsilon_{it}, \underbrace{\omega_{t}}_{\text{aggregate state}}) = \max_{j \in \{ 0, 1, ..., J \}} u^k (j, x_{jt}, \omega_{t}) + \varepsilon_{ijt} + \beta \mathbb{E} \left[ V^k(x_{it+1}, \varepsilon_{it+1}, \omega_{t+1}) \mid j, x_{it}, \varepsilon_{it} \right].\]

• If we assume \(\varepsilon_{ijt} \sim \text{T1EV}\), we can also get probability a type \(k\) household chooses \(j\), conditional on state \(x_{it}\): \(\mathbb{P}_{t}^k (j \mid x_{it})\).

• We can also denote \(\pi_t^k (j, \tau)\) as type \(k\)’s joint probability of living in location \(j\) with tenure \(\tau\) at the end of period \(t\).

• Then, type \(k\) population count for location \(j\) is: \(M_{jt}^k (\gamma_t, a_t) = \sum_\tau \pi_t^k (j, \tau) M_t^k \quad \forall k \in \{ 1, ...,K \}\).

Economic model 3-2: Housing demand (tourists)

\(\exists\) an exogenous number of tourists \(M_t^T\) arriving into the city and choosing to stay in a short-term rental or a hotel.

Tourists in short-term rentals

• Payoff for tourists in STR: \(u_{jt}^{ST} = \delta_j^{ST} + \delta_{t}^{ST} + \delta_p^{ST} \log p_{jt} + \delta_a^{ST} \log a_{jt} + \zeta_{jt}^{ST}.\)

• (number of tourists staying in STR): \(M_{jt}^{ST} (p_t, a_t) = \frac{\exp (u_{jt}^{ST})}{\sum_{j' = 0}^J \exp (u_{j't}^{ST})} \cdot M_t^T\).

Tourists in hotels

• Distribute total number of tourists in hotel in proportion to the hotel capacity observed in the data.

Economic model 4: Equilibrium

Population composition, rents, STR prices, and amenities are endogenously and jointly determined in stationary equilibrium.

Results: Amenities

Re-arranging equation in the model and taking logs: \(\log N_{sjt} = - \log F_{sjt}(N_{jt}) + \log \left( \sum_k \beta_s^k \phi^k \omega_t^k M_{jt}^k \right)\) Model-eq Identification

Estimation of \(\beta_s^k \equiv \alpha_s^k/\sigma^s\): Parameter that shows how population’s expenditure is allocated to each amenity sector \(s\).

Results: Housing demand

Results: Housing supply

Estimation: log difference between two supply choices

\[\log H_{jt}^{LT,S} - \log H_{jt}^{ST,S} = \alpha (\gamma_{jt} - p_{jt})+ \kappa_j + \kappa_t + \nu_{jt}\] model-eq Identification

(Brief) Counterfactuals and robustness checks

Counterfactuals

• Compare it with homogeneous preference specification: Less sorting, higher inequality.

• STR tax or a touristic amenities (TA) tax: Monotonic welfare increase for STR tax, but more nuanced for TA tax.

Robustness of real estate supply elasticity

• The paper’s main counterfactuals are robust to different supply elasticities, ranging from the baseline inelastic San Francisco case to the highly elastic case of Atlanta.

Comparison of static and dynamic model estimates

• Examine the impact of removing forward-looking behavior (\(\beta = 0\)) and location capital, i.e., the dynamic state-dependent component of moving costs.

• Most of the coefficients of the demand estimates become significantly different, hinting the importance of dynamic component in the model.

Conclusion

• This paper studies the role of preference heterogeneity over a set of endogenous location amenities in shaping within-city sorting and welfare inequality.

  • Build a model of residential choice where heterogeneous, forward-looking households consume a bundle of amenities provided by firms in a market for non-tradables.
  • Unlike past literature, the paper microfounds how different consumption amenities arise in equilibrium, endogenizing the extent to which neighborhoods become horizontally differentiated.

Empirical findings

• Heterogeneity in the preferences of residents and supply responses of firms are substantial.

• Distributional incidence of urban policies depends on heterogeneity on both demand and supply side of the amenities market.

APPENDIX

Housing supply inelasticity

• On average, annual growth of housing stock in Amsterdam is 1.2%, similar to the 0.9% value for San Francisco, one of the least housing-elastic cities in the US.

• Also, the assumption of inelastic housing supply is broadly in line with other studies of housing supply in the Netherlands (Vermeulen and Rouwendal, 2007).

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Identification of amenity

• Parameterize \(F_{sjt}(N_{jt}) = \Lambda_j \Lambda_t \cdot \underbrace{R(N_{jt})}_{\text{annual rental price of commercial real estate}} \cdot \Omega_{sjt}\)

• Assume \(R(N_{jt}) = N_{jt}^\eta\), where \(\eta\) is inverse supply elasticity of real-estate (calibrated).

• Identification issue: Amenity supply shock is correlated with \(N_{sjt}\) and \(M_{jt}^k\). We need amenity demand shifters as IV.

• The paper constructs an instrument that shift population composition: \(Z_{jt}^k = \omega_t^k \cdot\underbrace{S_{jt}^{\gamma(k)}}_{\text{housing stock by tenancy status}}\).

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Identification of housing supply

• OLS estimation leads to bias due to simultaneity bias from regressing quantities on prices.

• Use shift-share predicted tourist demand as IV.

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